A is the set of all points (x,y) in a plane, the difference of whose distances from two distinct fixed points is a positive constant.
Let's take a look at what this graph looks like. We get a set of points on a coordinate plane and the following two symmetric curves. Move the points along the curve.
Notice that here, the absolute value of the difference between the two fixed points for any point (x,y) in the set is 6. In general, the value can be any positive real number, as long as it is common for all the points in the set. We call the set of all points (x,y) with this property a hyperbola.
The word hyperbola comes from Greek hyperbolē which means excess or throwing beyond. The name reflects the way in which the curve extends indefinitely, seemingly exceeding the boundaries typical of other conic sections like the ellipse and the parabola. Let's complete the given statement.
A hyperbola is the set of all points (x,y) in a plane, the difference of whose distances from two distinct fixed points is a positive constant.
